Simplify the following expression: $\sqrt{150}+\sqrt{96}+\sqrt{54}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{150}+\sqrt{96}+\sqrt{54}$ $= \sqrt{25 \cdot 6}+\sqrt{16 \cdot 6}+\sqrt{9 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{6}+\sqrt{16} \cdot \sqrt{6}+\sqrt{9} \cdot \sqrt{6}$ $= 5\sqrt{6}+4\sqrt{6}+3\sqrt{6}$ Finally, simplify by combining the terms. $= ( 5 + 4 + 3 )\sqrt{6} = 12\sqrt{6}$